Geographic Information Systems now allow the use of analytic techniques in spatial epidemiology previously not feasible. As a result the mapping of routinely collected health data is now common and often provokes concern when patterns of disease rates appear to have "hot spots," although it is well understood by epidemiologists that the results may be biased by failure to collect and control for many known risk factors that are unevenly distributed over the area of the map;This project will refine the methods developed in the previous funding period for mapping data from case-control and cohort studies that adjust for these spatial confounders. An unexpected application of the spatial methods to the analysis of interactions in chemical mixtures will be explored in collaboration with the toxicology projects. As a second specific aim for understanding important epidemiologic patterns, this project will develop methods for assessing the direction and amount of bias occurring in group-level (ecologic) studies. Because they can use routinely collected group data, such studies are logistically easier to conduct but theoretically subject to serious error, although the magnitude of error in real data is not known. Methods for assessing these errors are important because there is potential for ecologic bias in partially ecologic studies that use a group-level measure of exposure (e.g., most studies of air and water pollution) and because of the hypothesis that certain group-level socioeconomic ("contextual") variables need to be included in otherwise individual-level studies. After developing methods for assessing these problems, we will apply them to real data from studies of Cape Cod, MA. Finally, the project will apply new methods from discrete mathematics to display the internal structure of data sets, especially the "small" data sets characteristic of hazardous waste investigations.